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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Quantum Field Theory 2

The course is not on the list Without time-table
Code Completion Credits Range Language
02KTPE2 Z,ZK 5 3+1 Czech
Lecturer:
Tutor:
Supervisor:
Department of Physics
Synopsis:

Symmetries, gauge fields, spontaneous symmetry breaking, quantization of relativistic fields, reduction formulas for S-matrix elements, perturbative series, Wick theorem, radiative corrections, renormalization.

Requirements:

Knowledge of the basic course of physics, quantum physics and Quantum field theory 1 lecture

Syllabus of lectures:

1. Lagrange formalism for free fields, symmetries and Noether theorem, space-time symmetries.

2. Gauge symmetries, non-abelian transformations, Young-Mills fields

3. Axial transformation, sigma model. Spontaneous symmetry breaking, Wigner and Goldstone modes. Explicit symmetry breaking.

4. Free scalar field, canonical commutator relations. Creation and annihilation operators, Hamiltonian, momentum and charge operators. Normal ordering, Fock space. Time-ordered products, Feynman propagator and microcausality.

5. Localized states, localized energy densities, vacuum fluctuations.

6. Quantization of free Dirac field.

Vector fields.

7. Interacting fields, (anti)commutation relations. Lehmann spectral decomposition, Young-Baxter equations.LSZ reduction formulas.

8. Perturbation series, Wick theorem, Feynman rules.

9. Several processes in tree approximation.

10. Diagrams with loops: self-energy, vacuum polarization.

11. Renormalization - general principles.

12. Renormalization of QED in one-loop.

Syllabus of tutorials:

1. Gauge symmetries, non-abelian transformations, Young-Mills fields

2. Axial transformation, sigma model. Explicit symmetry breaking.

3. Creation and annihilation operators, Hamiltonian, momentum and charge operators. Normal ordering, Fock space. Time-ordered products, Feynman propagator and microcausality.

4. Localized states, localized energy densities, vacuum fluctuations.

5. Interacting fields, (anti)commutation relations. Perturbation series, Wick theorem, Feynman rules.

6.Several processes in tree approximation, diagrams with loops: self-energy, vacuum polarization.

Study Objective:

Knowledge:

Symmetry and its violation, field quantization and S-matrix, perturbative expansion, renormalization

Abilities:

Active knowledge of field theory up to a level of one-loop renormalization of quantum electrodynamics

Study materials:

Key references:

[1] F. Gross: Relativistic Quantum Mechanics and Field Theory, Wiley-VCH, 1999; chapters 7-11

[2] J.D. Bjorken, S.D. Drell: Relativistic Quantum Fields, McGraw-Hill, 1965; chapters 11-17

[3] W. Greiner, J. Reinhardt: Field Quantization, Springer, 2008; chapters 4,5, 8 a 9

Recommended references:

[4] M.E. Peskin, D.V. Schroeder: An Introduction To Quantum Field Theory, Westview Press, 1995

[5] D.J. Griffiths: Introduction to Elementary Particles, John Wiley and sons, 1987

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2019-09-22
For updated information see http://bilakniha.cvut.cz/en/predmet1593806.html